Approximation schemes for monotone systems of nonlinear second order partial differential equations: convergence result and error estimate

We consider approximation schemes for monotone systems of fully nonlinear second order partial differential equations. We first prove a general convergence result for monotone, consistent and regular schemes. This result is a generalization to the well known framework of Barles-Souganidis, in the case of scalar nonlinear equation. Our second main result provides the convergence rate of approximation schemes for weakly coupled systems of Hamilton-Jacobi- Bellman equations. Examples including finite difference schemes and Semi-Lagrangian schemes are discussed.